A piezoresistive or capacitive sensor generates a change in electrical resistance or capacitance proportional to a physical force applied to it. Such sensors are commonly positioned on a silicon membrane to measure the deflection of the silicon membrane.
A number of problems arise in connection with the packaging of such sensors. For example, a silicon-based piezoresistive pressure sensor is attached to a package or substrate by means of a very soft, compliant adhesive, such that there is no residual stress or force transmitted from the package to the sensor. Should stress be transmitted to the sensor, the membrane of the sensor is deflected, creating a measured resistance value at the sensing element, which erroneously indicates a change in measured pressure. Stresses from the attachment process may add or subtract to this resistance change, depending upon the direction and magnitude of the pressure induced membrane deflection. In general, most commonly accepted calibration techniques adequately compensate for the non-ideal behavior of the pressure sensor caused by manufacturing variations and the necessity of attaching the sensor to a rigid base.
A problem with existing calibration techniques arises when the stresses from the attachment process change over time due to stress relief of the attachment material. This stress relief can be caused by exposure of the sensor, changes in the sensor surroundings, changes in the attachment material, and/or changes in the base to varying pressures and/or temperatures. Should the base, sensor, and attachment material not be closely matched in thermal expansion, then any temperature excursion produces a stress differential in the materials proportional to the difference in thermal expansion and temperature differential. In the case where the die attach material is a viscoelastic substance, it will flow over time in a fashion so as to decrease the stress. This will clearly have an impact on the piezoresistive membrane, changing the resistance value over time as well.
Typical calibration methods cannot account for the changing nature of the resistance values described above. The resistance of most sensors is a function of both temperature and pressure. One approach to model this physical activity is to use a polynomial equation of the form: EQU P=M.sub.0 +M.sub.1 *T+M.sub.2 *T.sup.2 +M.sub.3 *T.sup.3 +(M.sub.4 +M.sub.5 *T+M.sub.6 *T.sup.2 +M.sub.7 *T.sup.3)*V+(M.sub.8 +M.sub.9 *T+M.sub.10 *T.sup.2 +M.sub.11 *T.sup.3)*V.sup.2 +(M.sub.12 +M.sub.13 *T+M.sub.14 *T.sup.2 +M.sub.15 *T.sup.3)*V.sup.3 (Equation I)
P is the differential pressure applied across the membrane. Each M term is a derived coefficient. T is the temperature of the sensor membrane. V is the measure of the resistance of the sensor structure. For example, V may be the voltage produced by a constant current across the piezoresistive element.
The order of the polynomial required to fit a particular pressure sensor depends upon the individual manufacturing process, the attachment technique and the degree of accuracy required. A second order fit with respect to pressure and temperature commonly suffices, although a second order fit with respect to pressure and a third order fit with respect to temperature is sometimes required.
When a non-rigid die attach material is used, the M0 term of Equation I typically changes with time as well as temperature. This term is usually referred to as the "offset", referring to the fact that in most sensors when the pressure is "zero", there is no deflection on the membrane, but there is still a non-zero signal. This is true even for a sensor using a Wheatstone bridge resistor configuration which, ideally, may be designed to give a zero signal, but with manufacturing tolerances, will produce a small signal.
This aging phenomenon can create signal level shifts of approximately 0.5 psi. This shift or drift is relatively constant across the entire pressure range of interest. At a pressure level of 40 psi, this amounts to a 1.25% error, while at 5 psi, this amounts to a 10% error. Such errors are unacceptable in most applications.
It is not practical or acceptable for a customer to re-calibrate a pressure sensor which has drifted. Thus, it would be highly desirable to provide an improved sensing device that has the capability to correct drift. Ideally, such a sensor would automatically self-correct for drift in response to a relatively simple set of conditions invoked by a customer in the field. A thorough technique would compensate for drift factors, such as sensor aging, as a function of voltage and temperature conditions.